Note
Subclassing a numpy.ndarray is possible but if your goal is to create an array with modified behavior, as do dask arrays for distributed computation and cupy arrays for GPU-based computation, subclassing is discouraged. Instead, using numpy’s
is recommended.
The
can be inherited from (in Python or in C) if desired. Therefore, it can form a foundation for many useful classes. Often whether to sub-class the array object or to simply use the core array component as an internal part of a new class is a difficult decision, and can be simply a matter of choice. NumPy has several tools for simplifying how your new object interacts with other array objects, and so the choice may not be significant in the end. One way to simplify the question is by asking yourself if the object you are interested in can be replaced as a single array or does it really require two or more arrays at its core.
Note that
always returns the base-class ndarray. If you are confident that your use of the array object can handle any subclass of an ndarray, then
can be used to allow subclasses to propagate more cleanly through your subroutine. In principle, a subclass could redefine any aspect of the array and therefore, under strict guidelines,
would rarely be useful. However, most subclasses of the array object will not redefine certain aspects of the array object such as the buffer interface, or the attributes of the array. One important example, however, of why your subroutine may not be able to handle an arbitrary subclass of an array is that matrices redefine the “*” operator to be matrix-multiplication, rather than element-by-element multiplication.
Special attributes and methods
NumPy provides several hooks that classes can customize:
class.__array_ufunc__(ufunc, method, *inputs, **kwargs)
Any class, ndarray subclass or not, can define this method or set it to None in order to override the behavior of NumPy’s ufuncs. This works quite similarly to Python’s __mul__ and other binary operation routines.
ufunc is the ufunc object that was called.
method is a string indicating which Ufunc method was called (one of "__call__", "reduce", "reduceat", "accumulate", "outer", "inner").
inputs is a tuple of the input arguments to the ufunc.
kwargs is a dictionary containing the optional input arguments of the ufunc. If given, any out arguments, both positional and keyword, are passed as a
in kwargs. See the discussion in
for details.
The method should return either the result of the operation, or
if the operation requested is not implemented.
If one of the input, output, or where arguments has a
method, it is executed instead of the ufunc. If more than one of the arguments implements
, they are tried in the order: subclasses before superclasses, inputs before outputs, outputs before where, otherwise left to right. The first routine returning something other than
determines the result. If all of the
operations return
, a
is raised.
Note
We intend to re-implement numpy functions as (generalized) Ufunc, in which case it will become possible for them to be overridden by the __array_ufunc__ method. A prime candidate is
, which currently is not a Ufunc, but could be relatively easily be rewritten as a (set of) generalized Ufuncs. The same may happen with functions such as
,
, and
.
Like with some other special methods in python, such as __hash__ and __iter__, it is possible to indicate that your class does not support ufuncs by setting __array_ufunc__=None. Ufuncs always raise
when called on an object that sets __array_ufunc__=None.
The presence of
also influences how
handles binary operations like arr+obj and arr<obj when arr is an
and obj is an instance of a custom class. There are two possibilities. If obj.__array_ufunc__ is present and not None, then ndarray.__add__ and friends will delegate to the ufunc machinery, meaning that arr+obj becomes np.add(arr,obj), and then
invokes obj.__array_ufunc__. This is useful if you want to define an object that acts like an array.
Alternatively, if obj.__array_ufunc__ is set to None, then as a special case, special methods like ndarray.__add__ will notice this and unconditionally raise
. This is useful if you want to create objects that interact with arrays via binary operations, but are not themselves arrays. For example, a units handling system might have an object m representing the “meters” unit, and want to support the syntax arr*m to represent that the array has units of “meters”, but not want to otherwise interact with arrays via ufuncs or otherwise. This can be done by setting __array_ufunc__=None and defining __mul__ and __rmul__ methods. (Note that this means that writing an __array_ufunc__ that always returns
is not quite the same as setting __array_ufunc__=None: in the former case, arr+obj will raise
, while in the latter case it is possible to define a __radd__ method to prevent this.)
The above does not hold for in-place operators, for which
never returns
. Hence, arr+=obj would always lead to a
. This is because for arrays in-place operations cannot generically be replaced by a simple reverse operation. (For instance, by default, arr+=obj would be translated to arr=arr+obj, i.e., arr would be replaced, contrary to what is expected for in-place array operations.)
Note
If you define __array_ufunc__:
If you are not a subclass of
, we recommend your class define special methods like __add__ and __lt__ that delegate to ufuncs just like ndarray does. An easy way to do this is to subclass from
.
If you subclass
, we recommend that you put all your override logic in __array_ufunc__ and not also override special methods. This ensures the class hierarchy is determined in only one place rather than separately by the ufunc machinery and by the binary operation rules (which gives preference to special methods of subclasses; the alternative way to enforce a one-place only hierarchy, of setting
to None, would seem very unexpected and thus confusing, as then the subclass would not work at all with ufuncs).
defines its own
, which, evaluates the ufunc if no arguments have overrides, and returns
otherwise. This may be useful for subclasses for which
converts any instances of its own class to
: it can then pass these on to its superclass using super().__array_ufunc__(*inputs,**kwargs), and finally return the results after possible back-conversion. The advantage of this practice is that it ensures that it is possible to have a hierarchy of subclasses that extend the behaviour. See
for details.
class.__array_function__(func, types, args, kwargs)
func is an arbitrary callable exposed by NumPy’s public API, which was called in the form func(*args,**kwargs).
types is a collection
of unique argument types from the original NumPy function call that implement __array_function__.
The tuple args and dict kwargs are directly passed on from the original call.
As a convenience for __array_function__ implementers, types provides all argument types with an '__array_function__' attribute. This allows implementers to quickly identify cases where they should defer to __array_function__ implementations on other arguments. Implementations should not rely on the iteration order of types.
Most implementations of __array_function__ will start with two checks:
Is the given function something that we know how to overload?
Are all arguments of a type that we know how to handle?
If these conditions hold, __array_function__ should return the result from calling its implementation for func(*args,**kwargs). Otherwise, it should return the sentinel value NotImplemented, indicating that the function is not implemented by these types.
There are no general requirements on the return value from __array_function__, although most sensible implementations should probably return array(s) with the same type as one of the function’s arguments.
It may also be convenient to define a custom decorators (implements below) for registering __array_function__ implementations.
HANDLED_FUNCTIONS={}classMyArray:def__array_function__(self,func,types,args,kwargs):iffuncnotinHANDLED_FUNCTIONS:returnNotImplemented# Note: this allows subclasses that don't override# __array_function__ to handle MyArray objectsifnotall(issubclass(t,MyArray)fortintypes):returnNotImplementedreturnHANDLED_FUNCTIONS[func](*args,**kwargs)defimplements(numpy_function):"""Register an __array_function__ implementation for MyArray objects."""defdecorator(func):HANDLED_FUNCTIONS[numpy_function]=funcreturnfuncreturndecorator@implements(np.concatenate)defconcatenate(arrays,axis=0,out=None):...# implementation of concatenate for MyArray objects@implements(np.broadcast_to)defbroadcast_to(array,shape):...# implementation of broadcast_to for MyArray objectsNote that it is not required for __array_function__ implementations to include all of the corresponding NumPy function’s optional arguments (e.g., broadcast_to above omits the irrelevant subok argument). Optional arguments are only passed in to __array_function__ if they were explicitly used in the NumPy function call.
Just like the case for builtin special methods like __add__, properly written __array_function__ methods should always return NotImplemented when an unknown type is encountered. Otherwise, it will be impossible to correctly override NumPy functions from another object if the operation also includes one of your objects.
For the most part, the rules for dispatch with __array_function__ match those for __array_ufunc__. In particular:
NumPy will gather implementations of __array_function__ from all specified inputs and call them in order: subclasses before superclasses, and otherwise left to right. Note that in some edge cases involving subclasses, this differs slightly from the
of Python.
Implementations of __array_function__ indicate that they can handle the operation by returning any value other than NotImplemented.
If all __array_function__ methods return NotImplemented, NumPy will raise TypeError.
If no __array_function__ methods exists, NumPy will default to calling its own implementation, intended for use on NumPy arrays. This case arises, for example, when all array-like arguments are Python numbers or lists. (NumPy arrays do have a __array_function__ method, given below, but it always returns NotImplemented if any argument other than a NumPy array subclass implements __array_function__.)
One deviation from the current behavior of __array_ufunc__ is that NumPy will only call __array_function__ on the first argument of each unique type. This matches Python’s
rule for calling reflected methods
, and this ensures that checking overloads has acceptable performance even when there are a large number of overloaded arguments.
class.__array_finalize__(obj)
This method is called whenever the system internally allocates a new array from obj, where obj is a subclass (subtype) of the
. It can be used to change attributes of self after construction (so as to ensure a 2-d matrix for example), or to update meta-information from the “parent.” Subclasses inherit a default implementation of this method that does nothing.
class.__array_wrap__(array, context=None, return_scalar=False)
At the end of every
, this method is called on the input object with the highest array priority, or the output object if one was specified. The ufunc-computed array is passed in and whatever is returned is passed to the user. Subclasses inherit a default implementation of this method, which transforms the array into a new instance of the object’s class. Subclasses may opt to use this method to transform the output array into an instance of the subclass and update metadata before returning the array to the user.
NumPy may also call this function without a context from non-ufuncs to allow preserving subclass information.
Changed in version 2.0: return_scalar is now passed as either False (usually) or True indicating that NumPy would return a scalar. Subclasses may ignore the value, or return array[()] to behave more like NumPy.
Note
It is hoped to eventually deprecate this method in favour of
for ufuncs (and
for a few other functions like
).
class.__array_priority__
The value of this attribute is used to determine what type of object to return in situations where there is more than one possibility for the Python type of the returned object. Subclasses inherit a default value of 0.0 for this attribute.
Note
For ufuncs, it is hoped to eventually deprecate this method in favour of
.
class.__array__(dtype=None, copy=None)
If defined on an object, it must return a NumPy ndarray. This method is called by array-coercion functions like np.array() if an object implementing this interface is passed to those functions.
Third-party implementations of __array__ must take dtype and copy arguments.
Deprecated since version NumPy: 2.0 Not implementing copy and dtype is deprecated as of NumPy 2. When adding them, you must ensure correct behavior for copy.
dtype is the requested data type of the returned array and is passed by NumPy positionally (only if requested by the user). It is acceptable to ignore the dtype because NumPy will check the result and cast to dtype if necessary. If it is more efficient to coerce the data to the requested dtype without relying on NumPy, you should handle it in your library.
copy is a boolean passed by keyword. If copy=True you must return a copy. Returning a view into existing data will lead to incorrect user code. If copy=False the user requested that a copy is never made and you must raise an error unless no copy is made and the returned array is a view into existing data. It is valid to always raise an error for copy=False. The default copy=None (not passed) allows for the result to either be a view or a copy. However, a view return should be preferred when possible.
Please refer to
for the protocol hierarchy, of which __array__ is the oldest and least desirable.
Note
If a class (ndarray subclass or not) having the
method is used as the output object of an
, results will not be written to the object returned by
. This practice will return TypeError.
Example
Use __array__ to create a diagonal array of fixed size and value:
>>> importnumpyasnp>>> classDiagonalArray:... def__init__(self,N,value):... self._N=N... self._i=value... def__repr__(self):... returnf"{self.__class__.__name__}(N={self._N}, value={self._i})"... def__array__(self,dtype=None,copy=None):... ifcopyisFalse:... raiseValueError(... "`copy=False` isn't supported. A copy is always created."... )... returnself._i*np.eye(self._N,dtype=dtype)Our custom array can be instantiated like:
>>> arr=DiagonalArray(5,1)>>> arrDiagonalArray(N=5, value=1)We can convert to a numpy array using
or
, which will call its __array__ method to obtain a standard numpy.ndarray.
>>> np.asarray(arr)array([[1., 0., 0., 0., 0.], [0., 1., 0., 0., 0.], [0., 0., 1., 0., 0.], [0., 0., 0., 1., 0.], [0., 0., 0., 0., 1.]])Using dtype should return an appropriate ndarray or raise an error:
>>> np.asarray(arr,dtype=np.float32)array([[1., 0., 0., 0., 0.], [0., 1., 0., 0., 0.], [0., 0., 1., 0., 0.], [0., 0., 0., 1., 0.], [0., 0., 0., 0., 1.]], dtype=float32)If we operate on arr with a numpy function, numpy will again use the __array__ interface to convert it to an array and then apply the function in the usual way.
>>> np.multiply(arr,2)array([[2., 0., 0., 0., 0.], [0., 2., 0., 0., 0.], [0., 0., 2., 0., 0.], [0., 0., 0., 2., 0.], [0., 0., 0., 0., 2.]])Notice that the return type is a standard numpy.ndarray.
>>> type(np.multiply(arr,2))<class 'numpy.ndarray'>Matrix objects
Note
It is strongly advised not to use the matrix subclass. As described below, it makes writing functions that deal consistently with matrices and regular arrays very difficult. Currently, they are mainly used for interacting with scipy.sparse. We hope to provide an alternative for this use, however, and eventually remove the matrix subclass.
objects inherit from the ndarray and therefore, they have the same attributes and methods of ndarrays. There are six important differences of matrix objects, however, that may lead to unexpected results when you use matrices but expect them to act like arrays:
Matrix objects can be created using a string notation to allow Matlab-style syntax where spaces separate columns and semicolons (‘;’) separate rows.
Matrix objects are always two-dimensional. This has far-reaching implications, in that m.ravel() is still two-dimensional (with a 1 in the first dimension) and item selection returns two-dimensional objects so that sequence behavior is fundamentally different than arrays.
Matrix objects over-ride multiplication to be matrix-multiplication. Make sure you understand this for functions that you may want to receive matrices. Especially in light of the fact that asanyarray(m) returns a matrix when m is a matrix.
Matrix objects over-ride power to be matrix raised to a power. The same warning about using power inside a function that uses asanyarray(…) to get an array object holds for this fact.
The default __array_priority__ of matrix objects is 10.0, and therefore mixed operations with ndarrays always produce matrices.
Matrices have special attributes which make calculations easier. These are
Warning
Matrix objects over-ride multiplication, ‘*’, and power, ‘**’, to be matrix-multiplication and matrix power, respectively. If your subroutine can accept sub-classes and you do not convert to base- class arrays, then you must use the ufuncs multiply and power to be sure that you are performing the correct operation for all inputs.
The matrix class is a Python subclass of the ndarray and can be used as a reference for how to construct your own subclass of the ndarray. Matrices can be created from other matrices, strings, and anything else that can be converted to an ndarray . The name “mat “is an alias for “matrix “in NumPy.
Example 1: Matrix creation from a string
>>> importnumpyasnp>>> a=np.asmatrix('1 2 3; 4 5 3')>>> print((a*a.T).I) [[ 0.29239766 -0.13450292] [-0.13450292 0.08187135]]Example 2: Matrix creation from a nested sequence
>>> importnumpyasnp>>> np.asmatrix([[1,5,10],[1.0,3,4j]])matrix([[ 1.+0.j, 5.+0.j, 10.+0.j], [ 1.+0.j, 3.+0.j, 0.+4.j]])Example 3: Matrix creation from an array
>>> importnumpyasnp>>> np.asmatrix(np.random.rand(3,3)).Tmatrix([[4.17022005e-01, 3.02332573e-01, 1.86260211e-01], [7.20324493e-01, 1.46755891e-01, 3.45560727e-01], [1.14374817e-04, 9.23385948e-02, 3.96767474e-01]])Memory-mapped file arrays
Memory-mapped files are useful for reading and/or modifying small segments of a large file with regular layout, without reading the entire file into memory. A simple subclass of the ndarray uses a memory-mapped file for the data buffer of the array. For small files, the over-head of reading the entire file into memory is typically not significant, however for large files using memory mapping can save considerable resources.
Memory-mapped-file arrays have one additional method (besides those they inherit from the ndarray):
which must be called manually by the user to ensure that any changes to the array actually get written to disk.
Example:
>>> importnumpyasnp>>> a=np.memmap('newfile.dat',dtype=np.float64,mode='w+',shape=1000)>>> a[10]=10.0>>> a[30]=30.0>>> dela>>> b=np.fromfile('newfile.dat',dtype=np.float64)>>> print(b[10],b[30])10.0 30.0>>> a=np.memmap('newfile.dat',dtype=np.float64)>>> print(a[10],a[30])10.0 30.0Character arrays (
)
Note
The
class exists for backwards compatibility with Numarray, it is not recommended for new development. Starting from numpy 1.4, if one needs arrays of strings, it is recommended to use arrays of
,
or
, and use the free functions in the
module for fast vectorized string operations.
Deprecated since version 2.5: numpy.char.chararray is deprecated. Use an ndarray with a string or bytes dtype instead.
These are enhanced arrays of either
type or
type. These arrays inherit from the
, but specially-define the operations +, *, and % on a (broadcasting) element-by-element basis. These operations are not available on the standard
of character type. In addition, the
has all of the standard
(and
) methods, executing them on an element-by-element basis. Perhaps the easiest way to create a chararray is to use
where self is an ndarray of str or unicode data-type. However, a chararray can also be created using the
constructor, or via the
function:
Another difference with the standard ndarray of str data-type is that the chararray inherits the feature introduced by Numarray that white-space at the end of any element in the array will be ignored on item retrieval and comparison operations.
Record arrays
NumPy provides the
class which allows accessing the fields of a structured array as attributes, and a corresponding scalar data type object
.
Note
The pandas DataFrame is more powerful than record array. If possible, please use pandas DataFrame instead.
Masked arrays (
)
Standard container class
For backward compatibility and as a standard “container “class, the UserArray from Numeric has been brought over to NumPy and named
numpy.lib.user_array.container
The container class is a Python class whose self.array attribute is an ndarray. Multiple inheritance is probably easier with numpy.lib.user_array.container than with the ndarray itself and so it is included by default. It is not documented here beyond mentioning its existence because you are encouraged to use the ndarray class directly if you can.
Array iterators
Iterators are a powerful concept for array processing. Essentially, iterators implement a generalized for-loop. If myiter is an iterator object, then the Python code:
forvalinmyiter:...somecodeinvolvingval...calls val=next(myiter) repeatedly until
is raised by the iterator. There are several ways to iterate over an array that may be useful: default iteration, flat iteration, and \(N\)-dimensional enumeration.
Default iteration
The default iterator of an ndarray object is the default Python iterator of a sequence type. Thus, when the array object itself is used as an iterator. The default behavior is equivalent to:
foriinrange(arr.shape[0]):val=arr[i]This default iterator selects a sub-array of dimension \(N-1\) from the array. This can be a useful construct for defining recursive algorithms. To loop over the entire array requires \(N\) for-loops.
>>> importnumpyasnp>>> a=np.arange(24).reshape(3,2,4)+10>>> forvalina:... print('item:',val)item: [[10 11 12 13][14 15 16 17]]item: [[18 19 20 21][22 23 24 25]]item: [[26 27 28 29][30 31 32 33]]Flat iteration
As mentioned previously, the flat attribute of ndarray objects returns an iterator that will cycle over the entire array in C-style contiguous order.
>>> importnumpyasnp>>> fori,valinenumerate(a.flat):... ifi%5==0:print(i,val)0 105 1510 2015 2520 30Here, I’ve used the built-in enumerate iterator to return the iterator index as well as the value.
N-dimensional enumeration
Sometimes it may be useful to get the N-dimensional index while iterating. The ndenumerate iterator can achieve this.
>>> importnumpyasnp>>> fori,valinnp.ndenumerate(a):... ifsum(i)%5==0: print(i, val)(0, 0, 0) 10(1, 1, 3) 25(2, 0, 3) 29(2, 1, 2) 32Iterator for broadcasting
The general concept of broadcasting is also available from Python using the
iterator. This object takes \(N\) objects as inputs and returns an iterator that returns tuples providing each of the input sequence elements in the broadcasted result.
>>> importnumpyasnp>>> forvalinnp.broadcast([[1,0],[2,3]],[0,1]):... print(val)(np.int64(1), np.int64(0))(np.int64(0), np.int64(1))(np.int64(2), np.int64(0))(np.int64(3), np.int64(1))